# qiskit.algorithms.optimizers.L_BFGS_B¶

class L_BFGS_B(maxfun=1000, maxiter=15000, ftol=2.220446049250313e-15, factr=None, iprint=- 1, epsilon=1e-08, eps=1e-08, options=None, max_evals_grouped=1, **kwargs)[código fonte]

Limited-memory BFGS Bound optimizer.

The target goal of Limited-memory Broyden-Fletcher-Goldfarb-Shanno Bound (L-BFGS-B) is to minimize the value of a differentiable scalar function $$f$$. This optimizer is a quasi-Newton method, meaning that, in contrast to Newtons’s method, it does not require $$f$$’s Hessian (the matrix of $$f$$’s second derivatives) when attempting to compute $$f$$’s minimum value.

Like BFGS, L-BFGS is an iterative method for solving unconstrained, non-linear optimization problems, but approximates BFGS using a limited amount of computer memory. L-BFGS starts with an initial estimate of the optimal value, and proceeds iteratively to refine that estimate with a sequence of better estimates.

The derivatives of $$f$$ are used to identify the direction of steepest descent, and also to form an estimate of the Hessian matrix (second derivative) of $$f$$. L-BFGS-B extends L-BFGS to handle simple, per-variable bound constraints.

Uses scipy.optimize.fmin_l_bfgs_b. For further detail, please refer to https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html

Parâmetros
• maxfun (int) – Maximum number of function evaluations.

• maxiter (int) – Maximum number of iterations.

• ftol (float) – The iteration stops when (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= ftol.

• factr (Optional[float]) – (DEPRECATED) The iteration steps when (f^k - f^{k+1})/max{|f^k|, |f^{k+1}|,1} <= factr * eps, where eps is the machine precision, which is automatically generated by the code. Typical values for factr are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to ftol, which is exposed (instead of factr) by the scipy.optimize.minimize interface to L-BFGS-B.

• iprint (int) – Controls the frequency of output. iprint < 0 means no output; iprint = 0 print only one line at the last iteration; 0 < iprint < 99 print also f and |proj g| every iprint iterations; iprint = 99 print details of every iteration except n-vectors; iprint = 100 print also the changes of active set and final x; iprint > 100 print details of every iteration including x and g.

• eps (float) – If jac is approximated, use this value for the step size.

• epsilon (float) – (DEPRECATED) Step size used when approx_grad is True, for numerically calculating the gradient

• options (Optional[dict]) – A dictionary of solver options.

• max_evals_grouped (int) – Max number of default gradient evaluations performed simultaneously.

• kwargs – additional kwargs for scipy.optimize.minimize.

__init__(maxfun=1000, maxiter=15000, ftol=2.220446049250313e-15, factr=None, iprint=- 1, epsilon=1e-08, eps=1e-08, options=None, max_evals_grouped=1, **kwargs)[código fonte]
Parâmetros
• maxfun (int) – Maximum number of function evaluations.

• maxiter (int) – Maximum number of iterations.

• ftol (float) – The iteration stops when (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= ftol.

• factr (Optional[float]) – (DEPRECATED) The iteration steps when (f^k - f^{k+1})/max{|f^k|, |f^{k+1}|,1} <= factr * eps, where eps is the machine precision, which is automatically generated by the code. Typical values for factr are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to ftol, which is exposed (instead of factr) by the scipy.optimize.minimize interface to L-BFGS-B.

• iprint (int) – Controls the frequency of output. iprint < 0 means no output; iprint = 0 print only one line at the last iteration; 0 < iprint < 99 print also f and |proj g| every iprint iterations; iprint = 99 print details of every iteration except n-vectors; iprint = 100 print also the changes of active set and final x; iprint > 100 print details of every iteration including x and g.

• eps (float) – If jac is approximated, use this value for the step size.

• epsilon (float) – (DEPRECATED) Step size used when approx_grad is True, for numerically calculating the gradient

• options (Optional[dict]) – A dictionary of solver options.

• max_evals_grouped (int) – Max number of default gradient evaluations performed simultaneously.

• kwargs – additional kwargs for scipy.optimize.minimize.

Methods

 __init__([maxfun, maxiter, ftol, factr, …]) type maxfun int Return support level dictionary gradient_num_diff(x_center, f, epsilon[, …]) We compute the gradient with the numeric differentiation in the parallel way, around the point x_center. optimize(num_vars, objective_function[, …]) Perform optimization. Print algorithm-specific options. set_max_evals_grouped(limit) Set max evals grouped set_options(**kwargs) Sets or updates values in the options dictionary. wrap_function(function, args) Wrap the function to implicitly inject the args at the call of the function.

Attributes

 bounds_support_level Returns bounds support level gradient_support_level Returns gradient support level initial_point_support_level Returns initial point support level is_bounds_ignored Returns is bounds ignored is_bounds_required Returns is bounds required is_bounds_supported Returns is bounds supported is_gradient_ignored Returns is gradient ignored is_gradient_required Returns is gradient required is_gradient_supported Returns is gradient supported is_initial_point_ignored Returns is initial point ignored is_initial_point_required Returns is initial point required is_initial_point_supported Returns is initial point supported setting Return setting settings The optimizer settings in a dictionary format.
property bounds_support_level

Returns bounds support level

get_support_level()

Return support level dictionary

static gradient_num_diff(x_center, f, epsilon, max_evals_grouped=1)

We compute the gradient with the numeric differentiation in the parallel way, around the point x_center.

Parâmetros
• x_center (ndarray) – point around which we compute the gradient

• f (func) – the function of which the gradient is to be computed.

• epsilon (float) – the epsilon used in the numeric differentiation.

• max_evals_grouped (int) – max evals grouped

Retorna

Tipo de retorno

Returns gradient support level

property initial_point_support_level

Returns initial point support level

property is_bounds_ignored

Returns is bounds ignored

property is_bounds_required

Returns is bounds required

property is_bounds_supported

Returns is bounds supported

Returns is gradient ignored

Returns is gradient required

Returns is gradient supported

property is_initial_point_ignored

Returns is initial point ignored

property is_initial_point_required

Returns is initial point required

property is_initial_point_supported

Returns is initial point supported

optimize(num_vars, objective_function, gradient_function=None, variable_bounds=None, initial_point=None)

Perform optimization.

Parâmetros
• num_vars (int) – Number of parameters to be optimized.

• objective_function (callable) – A function that computes the objective function.

• gradient_function (callable) – A function that computes the gradient of the objective function, or None if not available.

• variable_bounds (list[(float, float)]) – List of variable bounds, given as pairs (lower, upper). None means unbounded.

• initial_point (numpy.ndarray[float]) – Initial point.

Retorna

point, value, nfev

point: is a 1D numpy.ndarray[float] containing the solution value: is a float with the objective function value nfev: number of objective function calls made if available or None

Levanta

ValueError – invalid input

print_options()

Print algorithm-specific options.

set_max_evals_grouped(limit)

Set max evals grouped

set_options(**kwargs)

Sets or updates values in the options dictionary.

The options dictionary may be used internally by a given optimizer to pass additional optional values for the underlying optimizer/optimization function used. The options dictionary may be initially populated with a set of key/values when the given optimizer is constructed.

Parâmetros

kwargs (dict) – options, given as name=value.

property setting

Return setting

property settings

The optimizer settings in a dictionary format.

The settings can for instance be used for JSON-serialization (if all settings are serializable, which e.g. doesn’t hold per default for callables), such that the optimizer object can be reconstructed as

settings = optimizer.settings
# JSON serialize and send to another server
optimizer = OptimizerClass(**settings)
Tipo de retorno

Dict[str, Any]

static wrap_function(function, args)

Wrap the function to implicitly inject the args at the call of the function.

Parâmetros
• function (func) – the target function

• args (tuple) – the args to be injected

Retorna

wrapper

Tipo de retorno

function_wrapper